Indentation behavior of the stiffest membrane mounted on a very compliant substrate: Graphene on PDMS

Graphene is the stiffest membrane and PDMS is one of the very compliant materials. The indentation response of a graphene monolayer mounted on a PDMS substrate (graphene/PDMS) is studied by both experimental and computational investigations. Due to the huge elastic modulus ratio between membrane and substrate (∼106) and the very large ratio of indentation depth to membrane thickness (∼103), the indentation deformation of graphene in the graphene/PDMS structure is analogous to that of free-standing (F-S) graphene but just with a relatively smaller indentation depth (i.e., the graphene deformation is insensitive to the appearance of PDMS substrate); the graphene can create a screening effect, which causes the PDMS substrate deformation to be insensitive to the tip geometry. In addition, with the aid of finite element method (FEM), the elastic modulus of graphene monolayer can be accurately determined from the overall indentation response of graphene/PDMS using an inverse analysis, which is determined as 0.982 TPa (very close to previously reported values). The present approach can be also extended to other 2D materials.